Optimal Ramp Schemes and Related Combinatorial Objects

In 1996, Jackson and Martin proved that a strong ideal ramp scheme is equivalent to an orthogonal array. However, there was no good characterization of ideal ramp schemes that are not strong. Here we show the equivalence of ideal ramp schemes to a new variant of orthogonal arrays that we term augmented orthogonal arrays. We give some constructions for these new kinds of arrays, and, as a consequence, we also provide parameter situations where ideal ramp schemes exist but strong ideal ramp schemes do not exist

A simple combinatorial treatment of constructions and threshold gaps of ramp schemes

We give easy proofs of some recent results concerning threshold gaps in ramp schemes. We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes. Finally, as an immediate consequence of these results, we provide a new explicit bound on the minimum length of a code having a specified distance and dual distance

Class Size Neo-Piagetian Testing: Theory, Results, and Implications

The main thrust of this study, therefore, revolved around the scale-up of the Case Instructional Sequence into a classroom size application able to be implemented by instructors with little additional practice in employing thistype of instructional sequence. Specifically, the purpose of this study was to determine the effect of the Case type treatment on the performance of two successive ninth grade physical science classes at a private, college-preparatory, secondary school in northeast Florida. These groups were to be assessed using the Tobin and Capie Test of Logical Thinking, a measure which could help assess their respective Piagetian stage

A Combinatorial Method for Discovery of BaTiO3-based Positive Temperature Coefficient Resistors

PhDThe conventional materials discovery is a kind of empirical (“trial and error”) science that of handling one sample at a time in the processes of synthesis and characterization. However, combinatorial methodologies present the possibility of a vastly increased rate of discovery of novel materials which will require a great deal of conventional laboratory work. The work presented in this thesis, involved the practice of a conceptual framework of combinatorial research on BaTiO3-based positive temperature coefficient resistor (PTCR) materials. Those including (i) fabrication of green BaTiO3 base discs via high-throughput dip-pen printing method. Preparation and formulation of BaTiO3 inks (selection of dispersant and binder/volume fraction) were studied. The shape of drying residues and the morphogenesis control of droplet drying were discussed. (ii) investigation of a fast droplet-doping method, which induced the dopant precursor solution infiltrating into the porous BT base disc. Various characterization methods were used to examine the dopant distribution in the body of disc. (iii) devising a high-throughput electrical measurement system including an integrated unit of temperature control and automatic measurement operation, and an arrayed multichannel jig. (iv) synthesis of donor-doped BaTiO3 libraries, which involved lanthanum, erbium, yttrium as donor elements and manganese as an acceptor dopant element respectively. Their temperature dependant resistivities were also explored. The work successfully developed an integrated tool including high-throughput synthesis of a large batch of libraries and high-throughput electrical property measurement for combinatorial research on BaTiO3-based PTCR ceramics. The Abstract ii combinatorial method, thus validated, has the potential to deliver dopant-doped BTbased PTCR libraries rapidly with a very wide range of dopant mixtures and concentrations for electrical property measurement and deserves to be applied to other low level dopant ceramic systems. These approaches are novel and paving the way for other new materials selection and materials research

Planning in constraint space for multi-body manipulation tasks

Robots are inherently limited by physical constraints on their link lengths, motor torques, battery power and structural rigidity. To thrive in circumstances that push these limits, such as in search and rescue scenarios, intelligent agents can use the available objects in their environment as tools. Reasoning about arbitrary objects and how they can be placed together to create useful structures such as ramps, bridges or simple machines is critical to push beyond one's physical limitations. Unfortunately, the solution space is combinatorial in the number of available objects and the configuration space of the chosen objects and the robot that uses the structure is high dimensional. To address these challenges, we propose using constraint satisfaction as a means to test the feasibility of candidate structures and adopt search algorithms in the classical planning literature to find sufficient designs. The key idea is that the interactions between the components of a structure can be encoded as equality and inequality constraints on the configuration spaces of the respective objects. Furthermore, constraints that are induced by a broadly defined action, such as placing an object on another, can be grouped together using logical representations such as Planning Domain Definition Language (PDDL). Then, a classical planning search algorithm can reason about which set of constraints to impose on the available objects, iteratively creating a structure that satisfies the task goals and the robot constraints. To demonstrate the effectiveness of this framework, we present both simulation and real robot results with static structures such as ramps, bridges and stairs, and quasi-static structures such as lever-fulcrum simple machines.Ph.D

Digital certificates and threshold cryptography

This dissertation discusses the use of secret sharing cryptographic protocols for distributing and sharing of secret documents, in our case PDF documents. We discuss the advantages and uses of such a system in the context of collaborative environments. Description of the cryptographic protocol involved and the necessary Public Key Infrastructure (PKI) shall be presented. We also provide an implementation of this framework as a “proof of concept” and fundament the use of a certificate extension as the basis for threshold cryptography. Details of the shared secret distribution protocol and shared secret recovery protocol shall be given as well as the associated technical implementation details. The actual secret sharing algorithm implemented at this stage is based on an existing well known secret sharing scheme that uses polynomial interpolation over a finite field. Finally we conclude with a practical assessment of our prototype

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set